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there are many pop sci articles and press releases wrt quantum computing these days and some may tend to stretch precision in description. one particular area that bothers me at the moment: some articles such as this statement from IBM [1] (and there are many other typical cases/ examples, maybe even some in papers/ books etc) say things in the form:

With a quantum computer built of just 50 qubits, none of today’s TOP500 supercomputers could successfully emulate it, reflecting the tremendous potential of this technology.

many researchers have been quoted making similar statements and they seem to be rarely backed by citations or details. now ofc this relates to the purity of the qubits and presumably claims like this are skipping the calculations that decrease capability based on error correction consuming some of the "qubit capability."

what is the scientific basis/ details for claims of the form, "x qubits could exceed classical computers of capability/ size y"?

now, am not at all questioning the general concept here shown decades ago that QM computers can in principle duplicate or outperform classical computers etc. but in other words, is there a rough estimate for # of qubits vs classical processor speed etc., what papers consider this question, what are the details of that calculation/ estimate? for answers, am willing to forego estimates of error correction, although would regard that as a bonus if available.

[1] IBM Makes Quantum Computing Available on IBM Cloud to Accelerate Innovation

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  • $\begingroup$ a subtlety: just because a supercomputer cannot emulate a qm computer as in 1st statement, does not mean that the qm computer could outperform that supercomputer on arbitrary calculations/ programs. the above claim by IBM was in the form of "classical machine with large capability y cannot emulate x qubits", but am particularly interested in analyzing other claims in the 2nd form. $\endgroup$ – vzn Dec 12 '16 at 4:20
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    $\begingroup$ For equivalence of the second form, the answer is 1 qubit = 1 bit, i.e. quantum computers have no advantage over classical computers on arbitrary computations. Only a handful of specific algorithms exist where quantum computing (QC) is believed to be better than classical computing, and hardly any of these are actually proven to be hard/impossible for classical computers. $\endgroup$ – Mark Mitchison Dec 12 '16 at 6:40

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